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Acta Optica Sinica, Volume. 44, Issue 2, 0212005(2024)

Linear Model of Inverse Kinematics for Non-Orthogonal Shafting Laser Theodolite

Zefeng Sun, Jiehu Kang*, Jian Liang, Zhen Zhang, Luyuan Feng, and Bin Wu**
Author Affiliations
  • State Key Laboratory of Precision Measurement Technology and Instruments, Tianjin University, Tianjin 300072, China
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    AbstractGet PDF(in Chinese)
    Figures&Tables (14)
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    References (24)
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    Figures & Tables(14)
    Structure of the non-orthogonal shafting laser theodolite

    Fig. 1. Structure of the non-orthogonal shafting laser theodolite

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    Principle of the non-orthogonal shafting laser theodolite

    Fig. 2. Principle of the non-orthogonal shafting laser theodolite

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    Initial estimate of the rotation angle

    Fig. 3. Initial estimate of the rotation angle

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    Simulation environment

    Fig. 4. Simulation environment

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    Simulation of the measured target points

    Fig. 5. Simulation of the measured target points

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    Calculation process

    Fig. 6. Calculation process

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    Simulation results of the rotation angle error

    Fig. 7. Simulation results of the rotation angle error

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    Non-orthogonal shafting theodolite prototype

    Fig. 8. Non-orthogonal shafting theodolite prototype

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    Experimental site

    Fig. 9. Experimental site

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    Aiming deviation

    Fig. 10. Aiming deviation

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    Experimental results of the rotation angle error

    Fig. 11. Experimental results of the rotation angle error

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    • Table 1. Shafting parameters

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      Table 1. Shafting parameters

      ShaftingVectorPoint coordinate /mm
      Vertical rotation axis（0，1，0）（0，0.081，0）
      Horizontal rotation axis（0.999999，0，-0.000328）（0，0，0）
      Laser axis（0.004097，0.999991，0.000549）（-0.511，0，-19.473）

    • Table 2. Simulation results of the rotation angles

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      Table 2. Simulation results of the rotation angles

      Simulation resultθ1θ2
      Mean error /mrad1.68×10-118.18×10-15
      RMSE（root mean square error）/mrad5.95×10-113.32×10-11

    • Table 3. Calculation results of the rotation angles

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      Table 3. Calculation results of the rotation angles

      Simulation resultθ1θ2
      Mean error /mrad0.0190.013
      RMSE /mrad0.0210.016
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    Zefeng Sun, Jiehu Kang, Jian Liang, Zhen Zhang, Luyuan Feng, Bin Wu. Linear Model of Inverse Kinematics for Non-Orthogonal Shafting Laser Theodolite[J]. Acta Optica Sinica, 2024, 44(2): 0212005

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    Paper Information

    Category: Instrumentation, Measurement and Metrology

    Received: Sep. 22, 2023

    Accepted: Nov. 8, 2023

    Published Online: Jan. 11, 2024

    The Author Email: Kang Jiehu (zhongdian313@163.com), Wu Bin (wubin@tju.edu.cn)

    DOI:10.3788/AOS231596

    Topics

    laser devices and laser physics
    Lasers and Laser Optics
    Laser physics
    laser manufacturing
    Instrumentation, Measurement and Metrology